Profit-Enhancing Parallel Imports

Abstract

We investigate competition between a domestic intellectual property right holder and a foreign imitator and consider how parallel imports affect their profits. We consider a two-country model. Country A is a developed country where intellectual property rights are highly protected, and country B is a developing country where protection is weak. The intellectual property right holder can sell the products for both markets while the imitator cannot export the products to country A. We find that permitting parallel imports can be beneficial for both players because it serves as a commitment device to soften price competition.

Keywords

Parallel imports Profits Intellectual property rights

We would like to thank an anonymous referee for careful and constructive comments. We would also like to thank Masahiro Ashiya, Fumio Dei, Wilfred Ethier, Naoko Nishimura, Yoshiyasu Ono, Koji Shimomura, Lex Zhao, and the seminar participants at the Research Institute for Economics and Business Administration at Kobe University. Needless to say, we are responsible for any remaining errors. The financial supports of the Grant-in-Aid from the Japan Securities Scholarship Foundation and from JSPS and MEXT are greatly appreciated.

where we use \(\tilde{\lambda} = 0\) and \(\tilde{p}_a^B + \tau =\tilde{p}_a^A=p_a^{A*}\) if τ = τ*. If the sign of Eq. 13 is minus, we obtain Lemma 1 because \(\tilde{\pi}_a\) is continuous. In other word, if \(\partial \tilde{p}_b^B/\partial \tau\) is negative, we obtain Lemma 1.

We now show that the sign of \(\partial \tilde{p}_b^B/\partial \tau\) is minus. To show it, we use the first-order conditions of the firms, that is, we use Eqs. 8, 9, and 11. Using Eqs. 8 and 9, we derive

The numerator of \(d \tilde{p}_b^B/d\tau\) is negative. The denominator of \(d \tilde{p}_b^B/d\tau\) is positive because A > B and D > C. Thus, \(d\tilde{p}_b^B/d\tau\) is negative. Therefore, Lemma 1 holds. □

Appendix 2

We now consider the case in which firm b also exports its product to country A at zero transport cost. We build a slightly modified model including the model mentioned in Section 2. The basic assumptions in this appendix are the same ones in Section 2 except the following ones. First, firm b also exports its product to country A at zero transport cost. Second, consumers in country A evaluate firm b’s product at hsb (h < 1). The assumption reflects that firm a is a world-wide famous firm but firm b is a domestic minor firm. Since firm b is not so familiar to consumers in country A, their evaluations for firm b’s product is smaller than sb. Third, we assume that F(θ) is the uniform distribution function of θ.

We first consider a case in which parallel imports are not permitted, that is, firm a can perfectly discriminate the markets. The profit maximization problems are as follows:

Second, we consider a case in which parallel imports are permitted. Obviously, firm a never chooses \(p_a^A > p_a^B + \tau\) because it induces parallel imports and reduces the profits of firm a. Thus, firm a faces the constraint, \(p_a^A \le p_a^B + \tau\). There exists the value of τ such that \(p_a^{A*} = p_a^{B*} + \tau\). We label the value as τ* ≡ 6(1 − h)s/((4 − s)(4 − hs)). If τ > τ*, the constraint \(p_a^A \le p_a^B + \tau\) is not binding, and whether parallel imports are permitted or not does not matter. We assume that τ ≤ τ*. Then, the profit maximization problems of the firms are as follows:

We now derive the condition that \(\tilde{\pi}_a - \pi_a^* > 0\). After several calculus, we find that if the following inequality is satisfied, there exists \(\tilde{\tau} (< \tau^*)\) such that for any \(\tau \in (\tilde{\tau}, \tau^*)\), \(\tilde{\pi}_a - \pi_a^* > 0\).

$$s_b < \frac{4\left(2(1+h)-\sqrt{4+h+4h^2}\right)}{7h}.$$

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Note that, h must be smaller than 1. If h = 1, there is no τ that satisfies \(\tilde{\pi}_a - \pi_a^* > 0\).

Appendix 3

We now consider the case in which θ is uniformly distributed over [0,1].

When τ ≥ 3sb/(2(4 − sb)), the constraint \(p_a^A \le p_a^B + \tau\) is not binding, and whether parallel imports are permitted or not does not matter. Therefore, 3sb − 2(4 − sb)τ is always positive, and then \(SW_B^n - SW_B^p > 0\).

References

Abbott FM (1998) First report (final) to the committee on international trade law of the international law association on the subject of parallel importation. J Int Econ Law 1:607–636CrossRefGoogle Scholar